Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | D3×#353 |
| Fitting | C3×#353 ⋊ C2 |
| Sylow | C3 ⋊ C2×#353 |
368 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 11 points:
(2,5)(3,8)(6,7)(9,10,11);(1,2)(3,6,8,5)(4,7);(10,11)39 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1402, #10715408, D3×#1408, … |
| maximal normal subgroup of | D3×#1402, #10715408, D3×#1408, … |
| maximal quotient of | D3×#1318, D3×#1325, #10704454, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1725);